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TREE(3) | Library Functions Manual | TREE(3) |
NAME¶
SPLAY_PROTOTYPE
,
SPLAY_GENERATE
,
SPLAY_ENTRY
,
SPLAY_HEAD
,
SPLAY_INITIALIZER
,
SPLAY_ROOT
,
SPLAY_EMPTY
,
SPLAY_NEXT
,
SPLAY_MIN
,
SPLAY_MAX
,
SPLAY_FIND
,
SPLAY_LEFT
,
SPLAY_RIGHT
,
SPLAY_FOREACH
,
SPLAY_INIT
,
SPLAY_INSERT
,
SPLAY_REMOVE
,
RB_PROTOTYPE
,
RB_PROTOTYPE_STATIC
,
RB_GENERATE
,
RB_GENERATE_STATIC
,
RB_ENTRY
,
RB_HEAD
,
RB_INITIALIZER
,
RB_ROOT
,
RB_EMPTY
,
RB_NEXT
,
RB_PREV
,
RB_MIN
,
RB_MAX
,
RB_FIND
,
RB_NFIND
,
RB_LEFT
,
RB_RIGHT
,
RB_PARENT
,
RB_FOREACH
,
RB_FOREACH_REVERSE
,
RB_INIT
,
RB_INSERT
,
RB_REMOVE
—
implementations of splay and red-black trees
SYNOPSIS¶
#include
<bsd/sys/tree.h>
SPLAY_PROTOTYPE
(NAME,
TYPE,
FIELD,
CMP);
SPLAY_GENERATE
(NAME,
TYPE,
FIELD,
CMP);
SPLAY_ENTRY
(TYPE);
SPLAY_HEAD
(HEADNAME,
TYPE);
struct TYPE *
SPLAY_INITIALIZER
(SPLAY_HEAD
*head);
SPLAY_ROOT
(SPLAY_HEAD
*head);
bool
SPLAY_EMPTY
(SPLAY_HEAD
*head);
struct TYPE *
SPLAY_NEXT
(NAME,
SPLAY_HEAD
*head, struct
TYPE *elm);
struct TYPE *
SPLAY_MIN
(NAME,
SPLAY_HEAD
*head);
struct TYPE *
SPLAY_MAX
(NAME,
SPLAY_HEAD
*head);
struct TYPE *
SPLAY_FIND
(NAME,
SPLAY_HEAD
*head, struct
TYPE *elm);
struct TYPE *
SPLAY_LEFT
(struct
TYPE *elm,
SPLAY_ENTRY
NAME);
struct TYPE *
SPLAY_RIGHT
(struct
TYPE *elm,
SPLAY_ENTRY
NAME);
SPLAY_FOREACH
(VARNAME,
NAME,
SPLAY_HEAD
*head);
void
SPLAY_INIT
(SPLAY_HEAD
*head);
struct TYPE *
SPLAY_INSERT
(NAME,
SPLAY_HEAD
*head, struct
TYPE *elm);
struct TYPE *
SPLAY_REMOVE
(NAME,
SPLAY_HEAD
*head, struct
TYPE *elm);
RB_PROTOTYPE
(NAME,
TYPE,
FIELD,
CMP);
RB_PROTOTYPE_STATIC
(NAME,
TYPE,
FIELD,
CMP);
RB_GENERATE
(NAME,
TYPE,
FIELD,
CMP);
RB_GENERATE_STATIC
(NAME,
TYPE,
FIELD,
CMP);
RB_ENTRY
(TYPE);
RB_HEAD
(HEADNAME,
TYPE);
RB_INITIALIZER
(RB_HEAD
*head);
struct TYPE *
RB_ROOT
(RB_HEAD
*head);
bool
RB_EMPTY
(RB_HEAD
*head);
struct TYPE *
RB_NEXT
(NAME,
RB_HEAD *head,
struct TYPE
*elm);
struct TYPE *
RB_PREV
(NAME,
RB_HEAD *head,
struct TYPE
*elm);
struct TYPE *
RB_MIN
(NAME,
RB_HEAD *head);
struct TYPE *
RB_MAX
(NAME,
RB_HEAD *head);
struct TYPE *
RB_FIND
(NAME,
RB_HEAD *head,
struct TYPE
*elm);
struct TYPE *
RB_NFIND
(NAME,
RB_HEAD *head,
struct TYPE
*elm);
struct TYPE *
RB_LEFT
(struct
TYPE *elm,
RB_ENTRY NAME);
struct TYPE *
RB_RIGHT
(struct
TYPE *elm,
RB_ENTRY NAME);
struct TYPE *
RB_PARENT
(struct
TYPE *elm,
RB_ENTRY NAME);
RB_FOREACH
(VARNAME,
NAME,
RB_HEAD *head);
RB_FOREACH_REVERSE
(VARNAME,
NAME,
RB_HEAD *head);
void
RB_INIT
(RB_HEAD
*head);
struct TYPE *
RB_INSERT
(NAME,
RB_HEAD *head,
struct TYPE
*elm);
struct TYPE *
RB_REMOVE
(NAME,
RB_HEAD *head,
struct TYPE
*elm);
DESCRIPTION¶
These macros define data structures for different types of trees: splay trees and red-black trees. In the macro definitions, TYPE is the name tag of a user defined structure that must contain a field of type SPLAY_ENTRY, or RB_ENTRY, named ENTRYNAME. The argument HEADNAME is the name tag of a user defined structure that must be declared using the macrosSPLAY_HEAD
(), or
RB_HEAD
(). The argument
NAME has to be a unique name prefix for every
tree that is defined.
The function prototypes are declared with
SPLAY_PROTOTYPE
(),
RB_PROTOTYPE
(), or
RB_PROTOTYPE_STATIC
(). The function bodies
are generated with SPLAY_GENERATE
(),
RB_GENERATE
(), or
RB_GENERATE_STATIC
(). See the examples
below for further explanation of how these macros are used.
SPLAY TREES¶
A splay tree is a self-organizing data structure. Every operation on the tree causes a splay to happen. The splay moves the requested node to the root of the tree and partly rebalances it. This has the benefit that request locality causes faster lookups as the requested nodes move to the top of the tree. On the other hand, every lookup causes memory writes. The Balance Theorem bounds the total access time for m operations and n inserts on an initially empty tree asO
((m + n)lg
n). The amortized cost for a sequence of
m accesses to a splay tree is
O
(lg n).
A splay tree is headed by a structure defined by the
SPLAY_HEAD
() macro. A structure is declared
as follows:
SPLAY_HEAD
(HEADNAME,
TYPE)
head;SPLAY_ENTRY
() macro declares a structure
that allows elements to be connected in the tree.
In order to use the functions that manipulate the tree structure, their
prototypes need to be declared with the
SPLAY_PROTOTYPE
() macro, where
NAME is a unique identifier for this
particular tree. The TYPE argument is the
type of the structure that is being managed by the tree. The
FIELD argument is the name of the element
defined by SPLAY_ENTRY
().
The function bodies are generated with the
SPLAY_GENERATE
() macro. It takes the same
arguments as the SPLAY_PROTOTYPE
() macro,
but should be used only once.
Finally, the CMP argument is the name of a
function used to compare tree nodes with each other. The function takes two
arguments of type struct TYPE *. If the first
argument is smaller than the second, the function returns a value smaller than
zero. If they are equal, the function returns zero. Otherwise, it should
return a value greater than zero. The compare function defines the order of
the tree elements.
The SPLAY_INIT
() macro initializes the tree
referenced by head.
The splay tree can also be initialized statically by using the
SPLAY_INITIALIZER
() macro like this:
SPLAY_HEAD
(HEADNAME,
TYPE) head =
SPLAY_INITIALIZER
(&head);SPLAY_INSERT
() macro inserts the new
element elm into the tree.
The SPLAY_REMOVE
() macro removes the element
elm from the tree pointed by
head.
The SPLAY_FIND
() macro can be used to find a
particular element in the tree.
struct TYPE find, *res; find.key = 30; res = SPLAY_FIND(NAME, head, &find);
SPLAY_ROOT
(),
SPLAY_MIN
(),
SPLAY_MAX
(), and
SPLAY_NEXT
() macros can be used to traverse
the tree:
for (np = SPLAY_MIN(NAME, &head); np != NULL; np = SPLAY_NEXT(NAME, &head, np))
SPLAY_FOREACH
() macro:
SPLAY_FOREACH
(np,
NAME,
head)SPLAY_EMPTY
() macro should be used to
check whether a splay tree is empty.
RED-BLACK TREES¶
A red-black tree is a binary search tree with the node color as an extra attribute. It fulfills a set of conditions:- Every search path from the root to a leaf consists of the same number of black nodes.
- Each red node (except for the root) has a black parent.
- Each leaf node is black.
O
(lg n).
The maximum height of a red-black tree is
2lg
(n +
1).
A red-black tree is headed by a structure defined by the
RB_HEAD
() macro. A structure is declared as
follows:
RB_HEAD
(HEADNAME,
TYPE)
head;RB_ENTRY
() macro declares a structure
that allows elements to be connected in the tree.
In order to use the functions that manipulate the tree structure, their
prototypes need to be declared with the
RB_PROTOTYPE
() or
RB_PROTOTYPE_STATIC
() macro, where
NAME is a unique identifier for this
particular tree. The TYPE argument is the
type of the structure that is being managed by the tree. The
FIELD argument is the name of the element
defined by RB_ENTRY
().
The function bodies are generated with the
RB_GENERATE
() or
RB_GENERATE_STATIC
() macro. These macros
take the same arguments as the
RB_PROTOTYPE
() and
RB_PROTOTYPE_STATIC
() macros, but should be
used only once.
Finally, the CMP argument is the name of a
function used to compare tree nodes with each other. The function takes two
arguments of type struct TYPE *. If the first
argument is smaller than the second, the function returns a value smaller than
zero. If they are equal, the function returns zero. Otherwise, it should
return a value greater than zero. The compare function defines the order of
the tree elements.
The RB_INIT
() macro initializes the tree
referenced by head.
The red-black tree can also be initialized statically by using the
RB_INITIALIZER
() macro like this:
RB_HEAD
(HEADNAME,
TYPE) head =
RB_INITIALIZER
(&head);RB_INSERT
() macro inserts the new element
elm into the tree.
The RB_REMOVE
() macro removes the element
elm from the tree pointed by
head.
The RB_FIND
() and
RB_NFIND
() macros can be used to find a
particular element in the tree.
struct TYPE find, *res; find.key = 30; res = RB_FIND(NAME, head, &find);
RB_ROOT
(),
RB_MIN
(),
RB_MAX
(),
RB_NEXT
(), and
RB_PREV
() macros can be used to traverse
the tree:
for (np = RB_MIN(NAME, &head); np
!= NULL; np = RB_NEXT(NAME, &head, np))
RB_FOREACH
() or
RB_FOREACH_REVERSE
() macro:
RB_FOREACH
(np,
NAME,
head)RB_EMPTY
() macro should be used to check
whether a red-black tree is empty.
NOTES¶
Trying to free a tree in the following way is a common error:SPLAY_FOREACH(var, NAME, head) { SPLAY_REMOVE(NAME, head, var); free(var); } free(head);
FOREACH
() macro refers to a pointer that
may have been reallocated already. Proper code needs a second variable.
for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) { nxt = SPLAY_NEXT(NAME, head, var); SPLAY_REMOVE(NAME, head, var); free(var); }
RB_INSERT
() and
SPLAY_INSERT
() return
NULL
if the element was inserted in the
tree successfully, otherwise they return a pointer to the element with the
colliding key.
Accordingly, RB_REMOVE
() and
SPLAY_REMOVE
() return the pointer to the
removed element otherwise they return NULL
to indicate an error.
SEE ALSO¶
queue(3)AUTHORS¶
The author of the tree macros is Niels Provos.December 27, 2007 | Debian |